BOLSINOV, A.V., IZOSIMOV, A. and TSONEV, D., 2016. Finite-dimensional integrable systems: a collection of research problems. Journal of Geometry and Physics, 115, pp. 2-15.
This article suggests a series of problems related to various algebraic and geometric
aspects of integrability. They reflect some recent developments in the theory of finite-dimensional integrable systems such as bi-Poisson linear algebra, Jordan-Kronecker invariants of finite dimensional Lie algebras, the interplay between singularities of Lagrangian fibrations and compatible Poisson brackets, and new techniques in projective geometry.
This paper was accepted for publication in the journal Journal of Geometry and Physics and the definitive published version is available at http://dx.doi.org/10.1016/j.geomphys.2016.11.003.